Accession Number:



Monte Carlo Studies of Continuous Hamiltonian Systems

Descriptive Note:

Final rept. 1 Sep 1996-30 Nov 2000

Corporate Author:


Personal Author(s):

Report Date:


Pagination or Media Count:



Under this grant, three main categories of research was conducted, all related to the correlation problem in Theoretical physics that arises from Many-Body interactions in Quantum Physics or from the effects of Multiple Scattering on Coherence. We have studied the Heisenberg Ferromagnet HF both in its classical and quantum versions. New details were obtained in the finite-size scaling relations of the HF that are tied to the issue of spontaneous symmetry breaking and the formation of Goldstone massless bosons-this was carried out using the celebrated Monte Carlo formalism on the classical HF. For the calculation of the Partition Function PF of the Quantum form of the HF. we have derived a new Theorem we call A Reduction Theorem which substantially reduces the number of matrix elements that contribute to the PF The Theorem is valid for any number of quantum HF spins. In particular we have also obtained closed analyticalalgebraic expressions of the Partition Function of up to four Quantum Heisenberg Spins. This result can be applied to any number of spins on any finite lattice in an approximation scheme that is still being explored. In essence, both the classical and quantum methods are needed to resolve some outstanding issues regarding the critical exponents of the HF. The finite-size scaling relations are also relevant to the nanotechnology driven issues related to nano-sized magnetism. The correlation problem also arises in the case of electron correlations in Condensed Matter when the bonding between atoms shows a strong redistribution of bonding orbitals upon condensation and the insertion of impurity atoms into the system, such as the insertion of Hydrogen into Nickel Aluminides. This we also have studied and made a contribution to via our earlier work on band structure theory where we showed clearly that the Full Potential in the Wigner-Seitz Cell must be taken into account for correct prediction of materials properties.

Subject Categories:

  • Optics
  • Quantum Theory and Relativity
  • Mechanics

Distribution Statement: